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# Did at least 15 percent of the children in Springfield suffer adverse

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Re: Did at least 15 percent of the children in Springfield suffer adverse [#permalink]
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Kudos
Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?

(1) Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.

For 80 boys and 20 girls
15% children = 15 children
20% girls = 4
10% boys = 8
Boys can be 9, in which case total affected children are less than 15

or
Boys can be 20, in which case total affected children are more than 15

Not sufficient

(2) Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.

Since both boys and girls are more than 15%, total children have to be more than 15%
Sufficient

Option B

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Did at least 15 percent of the children in Springfield suffer adverse [#permalink]
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Kudos
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Bunuel wrote:
Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?

(1) Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.

(2) Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.

Target question: Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?

Statement 1: Among the Springfield children, 20% of the girls and more than 10% of the boys suffered adverse effects after taking the vaccination.
This question tests an important (and often-tested) GMAT concept - weighted averages.

Let's say that 12% of the boys suffered adverse effects.
There are three possible scenarios to consider:
a) IF there were an EQUAL number of boys and girls, then the percentage of all children who suffered adverse effects would equal the average of 12% of 20%. So, the percentage of all children who suffered adverse effects would equal (20% + 12% )/2 = 16%
b) IF there were an MORE girls than boys, then the percentage of all children who suffered adverse effects would be closer to 20% than to 12%
c) IF there were an MORE boys than girls, then the percentage of all children who suffered adverse effects would be closer to 12% than to 20%

Now consider the following CONFLICTING cases
Case a: 20% of the girls suffered adverse effects, and 20% of the boys suffered adverse effects. If there are 2 girls and 2 boys, then 20% of all children suffered adverse effects.
Case b: 20% of the girls suffered adverse effects, and 11% of the boys suffered adverse effects. If there are 2 girls and 1000 boys, then the percentage of all children who suffered adverse effects will be very very close to 11%, since the boys have the bigger influence on the total percentage
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.
Since both groups (boys and girls) are such that EACH suffered more than 15% , then the COMBINED population is certain to have an adverse rate that's greater than 15%
Since we can answer the target question with certainty, statement 2 is SUFFICIENT